Graphs of Partitions

A partition of a number, say 9, is a sum like 4+2+1+1+1. That partition has these four partitions as parents, which are formed by merging pairs: 6+1+1+1, 5+2+1+1, 4+3+1+1, 4+2+2+1.

Create a graph by representing partitions as points and joining them to their parents. The thick view draws the graph with spheres and cylinders in 3D; in 2D the thick view labels the points with their partitions.